An Efficient Finite Difference Model For Flow In a Reservoir With Multiple Length-Scale Fractures

Abstract

We describe a hierarchical approach for modeling fluid flow in a naturally fractured reservoir with multiple length-scale fractures. Based on fracture length (lf) relative to the finite-difference grid size (lg), fractures are classified as belonging to one of three groups:short disconnected fractures (lf << lg),medium-length fractures (lf ~ lg), andlong fractures (lf >> lg). Effective grid-block permeabilities, associated with the short and medium length fractures, are used as input to a finite-difference simulator. We also present a separate transport equation for flow through long fractures to capture effects of large-scale high permeability pathways. Our new approach provides an improved means to include realistic and explicit fracture descriptions. Previously, Lough et al. (1997, 1998) developed a numerical method to compute the effective permeability of simulation grid-blocks with realistic fracture characterizations. Although this method handles generalized fracture geometries, it is numerically inefficient for the case where many small fractures exist. The method can also underestimate the flow contribution from long fractures. Assuming a linear potential gradient along the short fractures, we derive an analytical solution for the permeability contribution from short fractures. The solution becomes more accurate as fractures become randomly distributed and asymptotically small in length. The permeabilities from this analytical solution are used as the effective matrix permeability in computing a combined effective grid-block permeability that includes medium-length fractures. The method of Lough et al. is used for this computation. This hierarchical approach takes into account coupled flow between the rock matrix, short fractures and medium-length fractures. Long fractures are modeled explicitly in the reservoir simulator, using a transport equation that describes flow between long fractures and surrounding simulation grid-blocks. Simulation results from our new hierarchical approach are compared with those from the conventional dual porosity/permeability model. Numerical efficiency and accuracy are also examined.

Modelling of Conductive Faults with a Multiscale Approach

“…Fissured media can also be modelled by a single-medium model, see for instance the homogenization results by Lee et al (1999). It consists in considering equivalent permeabilities in a single-medium model, which take into account both the fissure and matrix media.…”

“…To model conductive faults, Lee et al (1999) proposed the well-like approach used in conventional reservoir simulators. They introduce a transport index, similar to the productivity index in well modelling, to formulate the fluid exchanges between the fault and the gridblock enclosing the fault.…”

A model for conductive faults with non-matching grids

“…This approach leads to the so-called interface model. Lee et al [18] followed a well-like approach, where the potential distribution is supposed to be at the hydrodynamic equilibrium. The fault volume is neglected in this model and therefore cannot take into account the distribution of several fluids inside the fault.…”

Upscaling of Oil-Water Displacement in Naturally Fractured Reservoirs

“…For the single continuum approach (5)(6)(7) , the system is considered as a heterogeneous matrix system with discrete fractures. Various methodologies, such as the boundary element and finite volume methods, are widely used to deal with complex fracture systems.…”